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Stability and positivity with respect to part of the variables for positive Markovian jump systems

Socha L.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 4

769--775

The stability and positivity of linear positive Markovian jump systems with respect to part of the variables is considered. The method-ologies of stability of positive systems with known transition probabilities based on common linear copositive Lyapunov function and stability of linear systems with respect to part of the variables are combined to find sufficient conditions of the stochastic stability and positivity of Markovian jump systems with respect to part of the variables. The results are extended for a class of nonlinear positive Markovian jump systems with respect to part of the variables. An example is given to illustrate the obtained results.

A new approach to robust ﬁnite-time H∞ control of continuous-time Markov jump systems

Yan S., Shen M., Fei S., Zhang G.

Control and Cybernetics

2015

Vol. 44, no. 2

211--231

This paper studies the robust ﬁnite-time H∞ state feedback control problem of continuous-time Markov jump systems (MJSs) subject to norm bounded uncertainties. Transition probabilities are allowed to be known, uncertain with known bounds or unknown. Based on the continuous transition probability property and the developed slack variable technique, Lyapunov variables are separatek from unknown transition probabilities and system matrices. With these separations, a relaxed method for robust ﬁnite-time H∞ controller design is proposed in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the eﬀectiveness of and the beneﬁt from the proposed method.